Your bronze will sparkle like the day you got them with the right cleaning technique. Here's the safe way that jewelers recommend.
Wipe the bronze item with a soft dry cloth to remove loose dust and debris before applying any cleaner.
Mix 1 tablespoon of salt, 1 tablespoon of baking soda, and the juice of half a lemon into a thick paste.
Rub the paste onto the bronze with a soft cloth or toothbrush. Work in small sections, scrubbing gently.
Allow the paste to sit for 1-2 minutes -- not longer, as the acid can affect the patina if you want to preserve it.
Rinse thoroughly with warm water to remove all paste. Dry immediately and completely with a soft cloth.